Wecken theorem for fixed and periodic points. (English) Zbl 1079.55007
Brown, R.F. (ed.) et al., Handbook of topological fixed point theory. Berlin: Springer (ISBN 1-4020-3221-8/hbk). 555-616 (2005).
The Nielsen conjecture on the Nielsen number \(N(f)\) is the following: There exists a map \(g\) homotopic to \(f\) such that Card(Fix\((g))=N(f)\). F. Wecken [Math. Ann. 117, 659–671 (1941; Zbl 0024.08405); Math. Ann. 118, 216–234 (1941; Zbl 0026.27103); Math. Ann. 118, 544–577 (1942; Zbl 0027.26503)] proved that this conjecture is true for self-maps \(f\) of manifolds of dimension at least three. In this paper the author surveys some generalizations of the Wecken theorem.
For the entire collection see [Zbl 1067.55001].
For the entire collection see [Zbl 1067.55001].
Reviewer: Ioan A. Rus (Cluj-Napoca)
MSC:
| 55M20 | Fixed points and coincidences in algebraic topology |
